Serious question to any atheist, what would make you believe in God, and do you believe the existence of a God is possible?
Since you write god with a capital g, I will assume your questions are more limited than what you actually wrote, and that you're primarily concerned with belief in the Christian God. I'll try to answer for both meanings though.
First of all, the understanding of what the terms 'god' and 'God' means should be agreed upon. I found these on Wikipedia:
Wikipedia: God
God is the English name given to a singular being in theistic and deistic religions (and other belief systems) who is either the sole deity in monotheism, or a single deity in polytheism.
Wikipedia: Deity:
A deity is a recognised preternatural or supernatural immortal being, who may be thought of as holy, divine, or sacred, held in high regard, and respected by believers, often religiously referred to as a god.
While we could discuss the meanings for an unlimited number of threads, I'll just go off with two examples on either extreme.
In the first case, a god could be anyone or anything who is (understood to be) immortal and who has powers beyond what a mere human has: Being able to jump 50 meters in the air for instance.
I suppose it is within the realms of the possible that such a being can exist, and for believing in it I would have to see that it is able to accomplish what it claims it can do. In this case: A scientific test where one tries to kill the being, and another scientific test to verify that it can also jump as high as it claims. Of course, I'm not sure I would find any need to worship such a being even if I believed in it, nor is it certain I would feel like actually calling it a god.
In the second case, a god like you were initially addressing, is a conscious, immortal being with a personality and absolutely unlimited powers, who has created everything except for itself, and take an interest in what even the smallest conscious being within his creation.
Is it possible that such a being exists? I don't know. The claims of what it can do are so grandiose that it should initially seem quite unlikely. But of course, one can't prove that it doesn't exist just because there is no reason to believe it exists. So I'd say I find the likelihood of such a being to exist to be as close to zero as is possible.
What would make me believe in such a being? A good question. First of all, scientific tests would still be required. But because of the unlimited things such a being claim to be able to do, it is impossible to verify all of them. At one point one would simply accept the word of the being and assume that it can in fact do all the other things it claims to be able to do. But to give you a list:
- It should first acknowledge to us that it exists, for instance by shining some huge light down on people and saying: "I am. I exist." or something like that.
- After explaining what he is and who he is, he could then start by setting everything about his religion(s) straight: Which denomination is the right one (some form of Judaism, Christianity or Islam?), and also retell the holy books and clear up and misunderstandings and contradictions. If this explanation does not coincide with scientific knowledge, explanations as to why that is should be given.
- Explain how he came into being, and most likely give us an understanding of space-time, the possible beginnings or ends of the universe and reality, and such.
- Finally, as all we have as of yet is an intangible being with lots of knowledge and claims, we must of course test the claims about his abilities:
1. Do something completely outlandish, like, turn all the iron and rocks of the earth into marshmallows in an instant and maintain the lives of all the beings on earth during the experiment. Then turn everything back again, minus the marshmallow that has now been eaten.
2. Showing that Heaven and Hell exists, and that there is a life after death.
3. Proving that he can in fact create universes by actually demonstrating that he can do so.
4. Create at least one adult human being out of nothingness, and make sure this human is ready to be a fully functional member of current society with no psychological issues from suddenly having been created.
Then I'll believe that God exists.
How would I know? There are billions of different possibilities out there for a supernatural being or force. 
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